Initial phase determination in a wave

[Jos_Moreira]

Homework Statement

I'm having trouble solving the following exercise:
Given the following wave equation:
y=0.01cos(wt-kx)+0.02*6^(1/2)sin(wt-kx)
prove that if w=16s^-1 and k=6m^-1 then the amplitude of the wave is 0.05 meters and the initial phase is -pi/4 how can I prove that? By phasor addiction probably but I can't go far that way. can someone show me how to do it?
Thank you

Homework Equations

The Attempt at a Solution

I converted sin(wt-kx) to cos(wt-kx-pi/2) so I can write the phasor corresponding to each cosine and attempt to add then an see what I get back, but what I get back I the equation I started with with the cos(wt-kx-pi/2) back as sin(wt-kx) by looking att the trignometric identity: acos(A)+bsin(B)=$$\sqrt{b^2+a^2}$$*sin(A+C) where C is arctan($$\frac{b}{a}$$) i could get the amplitude, but the phase I get is diffrent.

 

[hy23]

can't you use trig to turn cos(A-B) into cosAcosB+sinAsinB, turn sin(A-B) to sinAcosB-cosAsinB